Journal of Statistical Physics, Vol. 73, Nos. 5/6, 1993. p. 879-892.
The diffusion-limited reaction A + A <-> A + B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis in d = 1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously
studied reaction A +A <-> A. For d > 1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work in d = 1, 2, and 3.